Theory of activated rate processes in the weak and intermediate friction cases: New analytical results for one and many degrees of freedom

Abstract

Simple analytical expressions for the reaction rate of activated rate processes are derived in the weak/intermediate friction limit for one and many degrees of freedom and for finite microcanonical reaction rates. The expressions are obtained by analytical solution of the steady-state integral master equations (in energy variables). The microcanonical reaction rate is taken to be independent of energy (higher than the activation energy). Irreversible transitions from one state and reversible transitions between many states are discussed in detail. A simple interpolation formula for the reaction rate is derived which describes a turnover from the weak friction regime to a strong friction one. The formula takes into account an interplay between activation and reaction at energies close to the activation energy. When applied to unimolecular gas phase reactions this interpolation formula bridges between the weak and strong collision limits. The formulas obtained are generalized to multidimensional activated rate processes.